Introduction
Wireless communications systems are becoming increasingly important worldwide. Wireless cellular telecommunications systems are rapidly replacing conventional wire-based telecommunications systems in many applications. Cellular radio telephone networks (“CRT”), and specialized mobile radio and mobile data radio networks are examples. The general principles of wireless cellular telephony have been described variously, for example in U.S. Pat. No. 5,295,180 to Vendetti, et al, which is incorporated herein by reference.
There is great interest in using existing infrastructures for wireless communication systems for locating people and/or objects in a cost effective manner. Such a capability would be invaluable in a variety of situations, especially in emergency or crime situations. Due to the substantial benefits of such a location system, several attempts have been made to design and implement such a system.
Systems have been proposed that rely upon signal strength and trilateralization techniques to permit location include those disclosed in U.S. Pat. Nos. 4,818,998 and 4,908,629 to Apsell et al. (“the Apsell patents”) and 4,891,650 to Sheffer (“the Sheffer patent”). However, these systems have drawbacks that include high expense in that special purpose electronics are required. Furthermore, the systems are generally only effective in line-of-sight conditions, such as rural settings. Radio wave surface reflections, refractions and ground clutter cause significant distortion, in determining the location of a signal source in most geographical areas that are more than sparsely populated. Moreover, these drawbacks are particularly exacerbated in dense urban canyon (city) areas, where errors and/or conflicts in location measurements can result in substantial inaccuracies.
Another example of a location system using time of arrival and triangulation for location are satellite-based systems, such as the military and commercial versions of the Global Positioning Satellite system (“GPS”). GPS can provide accurate position determination (i.e., about 100 meters error for the commercial version of GPS) from a time-based signal received simultaneously from at least three satellites. A ground-based GPS receiver at or near the object to be located determines the difference between the time at which each satellite transmits a time signal and the time at which the signal is received and, based on the time differentials, determines the object's location. However, the GPS is impractical in many applications. The signal power levels from the satellites are low and the GPS receiver requires a clear, line-of-sight path to at least three satellites above a horizon of about 60 degrees for effective operation. Accordingly, inclement weather conditions, such as clouds, terrain features, such as hills and trees, and buildings restrict the ability of the GPS receiver to determine its position. Furthermore, the initial GPS signal detection process for a GPS receiver is relatively long (i.e., several minutes) for determining the receiver's position. Such delays are unacceptable in many applications such as, for example, emergency response and vehicle tracking.
Differential GPS, or DGPS systems offer correction schemes to account for time synchronization drift. Such correction schemes include the transmission of correction signals over a two-way radio link or broadcast via FM radio station subcarriers. These systems have been found to be awkward and have met with limited success.
Additionally, GPS-based location systems have been attempted in which the received GPS signals are transmitted to a central data center for performing location calculations. Such systems have also met with limited success. In brief, each of the various GPS embodiments have the same fundamental problems of limited reception of the satellite signals and added expense and complexity of the electronics required for an inexpensive location mobile station or handset for detecting and receiving the GPS signals from the satellites.
Radio Propagation Background
The behavior of a mobile radio signal in the general environment is unique and complicated. Efforts to perform correlations between radio signals and distance between a base station and a mobile station are similarly complex. Repeated attempts to solve this problem in the past have been met with only marginal success. Factors include terrain undulations, fixed and variable clutter, atmospheric conditions, internal radio characteristics of cellular and PCS systems, such as frequencies, antenna configurations, modulation schemes, diversity methods, and the physical geometries of direct, refracted and reflected waves between the base stations and the mobile. Noise, such as man-made externally sources (e.g., auto ignitions) and radio system co-channel and adjacent channel interference also affect radio reception and related performance measurements, such as the analog carrier-to-interference ratio (C/I), or digital energy-per-bit/Noise density ratio (Eb/No) and are particular to various points in time and space domains.
RF Propagation in Free Space
Before discussing real world correlations between signals and distance, it is useful to review the theoretical premise, that of radio energy path loss across a pure isotropic vacuum propagation channel, and its dependencies within and among various communications channel types. FIG. 1 illustrates a definition of channel types arising in communications: Over the last forty years various mathematical expressions have been developed to assist the radio mobile cell designer in establishing the proper balance between base station capital investment and the quality of the radio link, typically using radio energy field-strength, usually measured in microvolts/meter, or decibels.
First consider Hata's single ray model. A simplified radio channel can be described as:Gi=Lp+F+Lf+Lm+Lb−Gt+Gr  (Equation 1)where Gi=system gain in decibels                Lp=free space path loss in dB,        F=fade margin in dB,        Lf=transmission line loss from coaxials used to connect radio to antenna, in dB,        Lm=miscellaneous losses such as minor antenna misalignment, coaxial corrosion, increase in the receiver noise figure due to aging, in dB,        Lb=branching loss due to filter and circulator used to combine or split transmitter and receiver signals in a single antenna        Gt=gain of transmitting antenna        Gr=gain of receiving antennaFree space path loss1 Lp as discussed in Mobile Communications Design Fundamentals, William C. Y. Lee, 2nd, Ed across the propagation channel is a function of distance d, frequencyf (for f values<1 GHz, such as the 890–950 mHz cellular band):        
                                          P            or                                P            t                          =                  1                                    (                              4                ⁢                π                ⁢                                                                  ⁢                dfc                            )                        2                                              (equation  2)            where Por=received power in free space                Pt=transmitting power        c=speed of light,The difference between two received signal powers in free space,        
                              Δ          p                =                                            (              10              )                        ⁢            log            ⁢                                                  ⁢                          (                                                p                  or2                                                  p                  or1                                            )                                =                                    (              20              )                        ⁢            log            ⁢                                                  ⁢                          (                                                d                  1                                                  d                  2                                            )                        ⁢                          (              dB              )                                                          (equation  3)            indicates that the free propagation path loss is 20 dB per decade. Frequencies between 1 GHz and 2 GHz experience increased values in the exponent, ranging from 2 to 4, or 20 to 40 dB/decade, which would be predicted for the new PCS 1.8–1.9 GHz bandThis suggests that the free propagation path loss is 20 dB per decade. However, frequencies between 1 GHz and 2 GHz experience increased values in the exponent, ranging from 2 to 4, or 20 to 40 dB/decade, which would be predicted for the new PCS 1.8–1.9 GHz band. One consequence from a location perspective is that the effective range of values for higher exponents is an increased at higher frequencies, thus providing improved granularity of ranging correlation.Environmental Clutter and RF Propagation Effects
Actual data collected in real-world environments uncovered huge variations with respect to the free space path loss equation, giving rise to the creation of many empirical formulas for radio signal coverage prediction. Clutter, either fixed or stationary in geometric relation to the propagation of the radio signals, causes a shadow effect of blocking that perturbs the free space loss effect. Perhaps the best known model set that characterizes the average path loss is Hata's, “Empirical Formula for Propagation Loss in Land Mobile Radio”, M. Hata, IEEE Transactions VT-29, pp. 317–325, August 1980, three pathloss models, based on Okumura's measurements in and around Tokyo, “Field Strength and its Variability in VHF and UHF Land Mobile Service”, Y. Okumura, et al, Review of the Electrical Communications laboratory, Vol 16, pp 825–873, September–October 1968.
The typical urban Hata model for Lp was defined as Lp=Lhu:LHu=69.55+26.16 log(f)−13.82 log(hBS)−a(hMS)+((44.9−6.55 log(HBS) log(d)[dB])  (Equation 4)where LHu=path loss, Hata urban                hBS=base station antenna height        hMS=mobile station antenna height        d=distance BS-MS in km        a(hMS) is a correction factor for small and medium sized cities, found to be:1 log(f−0.7)hMS−1.56 log(f−0.8)=a(hMS)  (Equation 5)For large cities the correction factor was found to be:a(hMS)=3.2[log 11.75 hMS]2−4.97  (Equation 6)assuming f is equal to or greater than 400 mHz.        
The typical suburban model correction was found to be:
                              L                      H            suburban                          =                              L            Hu                    -                      2            ⁡                          [                              log                ⁢                                                                  ⁢                                                      (                                          f                      28                                        )                                    2                                            ]                                -                      5.4            ⁢                                                  [            dB            ]                                              (Equation  7)            
The typical rural model modified the urban formula differently, as seen below:LHrural=LHu−4.78 (log f)2+18.33 log f−40.94[dB]  (Equation 8)
Although the Hata model was found to be useful for generalized RF wave prediction in frequencies under 1 GHz in certain suburban and rural settings, as either the frequency and/or clutter increased, predictability decreased. In current practice, however, field technicians often have to make a guess for dense urban an suburban areas (applying whatever model seems best), then installing a base stations and begin taking manual measurements. Coverage problems can take up to a year to resolve.
Relating Received Signal Strength to Location
Having previously established a relationship between d and Por, reference equation 2 above: d represents the distance between the mobile station (MS) and the base station (BS); Por represents the received power in free space) for a given set of unchanging environmental conditions, it may be possible to dynamically measure Por and then determine d.
In 1991, U.S. Pat. No. 5,055,851 to Sheffer taught that if three or more relationships have been established in a triangular space of three or more base stations (BSs) with a location database constructed having data related to possible mobile station (MS) locations, then arculation calculations may be performed, which use three distinct Por measurements to determine an X,Y, two dimensional location, which can then be projected onto an area map. The triangulation calculation is based on the fact that the approximate distance of the mobile station (MS) from any base station (BS) cell can be calculated based on the received signal strength. Sheffer acknowledges that terrain variations affect accuracy, although as noted above, Sheffer's disclosure does not account for a sufficient number of variables, such as fixed and variable location shadow fading, which are typical in dense urban areas with moving traffic.
Most field research before about 1988 has focused on characterizing (with the objective of RF coverage prediction) the RF propagation channel (i.e., electromagnetic radio waves) using a single-ray model, although standard fit errors in regressions proved dismal (e.g., 40–80 dB). Later, multi-ray models were proposed, and much later, certain behaviors were studied with radio and digital channels. In 1981, Vogler proposed that radio waves at higher frequencies could be modeled using optics principles. In 1988 Walfisch and Bertoni applied optical methods to develop a two-ray model, which when compared to certain highly specific, controlled field data, provided extremely good regression fit standard errors of within 1.2 dB.
In the Bertoni two ray model it was assumed that most cities would consist of a core of high-rise buildings surrounded by a much larger area having buildings of uniform height spread over regions comprising many square blocks, with street grids organizing buildings into rows that are nearly parallel. Rays penetrating buildings then emanating outside a building were neglected. FIG. 2 provides a basis for the variables.
After a lengthy analysis it was concluded that path loss was a function of three factors: (1) the path loss between antennas in free space; (2) the reduction of rooftop wave fields due to settling; and (3) the effect of diffraction of the rooftop fields do to ground level. The last two factors were summarily termed Lex, given by:
                                                                        L                ex                            =                            ⁢                              57.1                +                A                +                                  log                  ⁡                                      (                    f                    )                                                  +                R                -                                  (                                                            (                                              18                        ⁢                                                                                                  ⁢                        log                        ⁢                                                                                                  ⁢                                                  (                          H                          )                                                                    )                                        -                                                                                                                                        ⁢                              18                ⁢                                                                  ⁢                                  log                  ⁢                                                                          [                                      1                    -                                                                  R                        2                                                                    17                        ⁢                        H                                                                              ]                                                                                        (Equation  9)            The influence of building geometry is contained in A:
                                                        A                                      =                                                                        5                  ⁢                                      log                    ⁢                                                                                  [                                                                  d                        2                                            2                                        ]                                                  -                                  9                  ⁢                  log                  ⁢                                                                          ⁢                  d                                +                                                                                                                                                                                                                                20                ⁢                                                                  ⁢                log                ⁢                                                                  ⁢                                  {                                                            tan                      ⁢                                                                                          [                                              2                        ⁢                                                                                                  ⁢                                                  (                                                      h                            -                                                          H                              MS                                                                                )                                                                    ]                                                              -                      1                                                        }                                                                    ⁢                                                      (                  Equation          ⁢                                          ⁢          10                )            
However, a substantial difficulty with the two-ray model in practice is that it requires a substantial amount of data regarding building dimensions, geometries, street widths, antenna gain characteristics for every possible ray path, etc. Additionally, it requires an inordinate amount of computational resources and such a model is not easily updated or maintained.
Unfortunately, in practice clutter geometries and building heights are random. Moreover, data of sufficient detail has been extremely difficult to acquire, and regression standard fit errors are poor; i.e., in the general case, these errors were found to be 40–60 dB. Thus the two-ray model approach, although sometimes providing an improvement over single ray techniques, still did not predict RF signal characteristics in the general case to level of accuracy desired (<10 dB).
Work by Greenstein has since developed from the perspective of measurement-based regression models, as opposed to the previous approach of predicting-first, then performing measurement comparisons. Apparently yielding to the fact that low-power, low antenna (e.g., 12–25 feet above ground) height PCS microcell coverage was insufficient in urban buildings, Greenstein, et al, authored “Performance Evaluations for Urban Line-of-sight Microcells Using a Multi-ray Propagation Model”, in IEEE Globecom Proceedings, December 1991. This paper proposed the idea of formulating regressions based on field measurements using small PCS microcells in a lineal microcell geometry (i.e., geometries in which there is always a line-of-sight (LOS) path between a subscriber's mobile and its current microsite).
Additionally, Greenstein studied the communication channels variable Bit-Error-Rate (BER) in a spatial domain, which was a departure from previous research that limited field measurements to the RF propagation channel signal strength alone. However, Greenstein based his finding on two suspicious assumptions: 1) he assumed that distance correlation estimates were identical for uplink and downlink transmission paths; and 2) modulation techniques would be transparent in terms of improved distance correlation conclusions. Although some data held very correlations, other data and environments produced poor results. Accordingly, his results appear unreliable for use in general location context.
In 1993 Greenstein, et al, authored “A Measurement-Based Model for Predicting Coverage Areas of Urban Microcells”, in the IEEE Journal On Selected Areas in Communications, Vol. 11, No. 7, September 1993. Greenstein reported a generic measurement-based model of RF attenuation in terms of constant-value contours surrounding a given low-power, low antenna microcell environment in a dense, rectilinear neighborhood, such as New York City. However, these contours were for the cellular frequency band. In this case, LOS and non-LOS clutter were considered for a given microcell site. A result of this analysis was that RF propagation losses (or attenuations), when cell antenna heights were relatively low, provided attenuation contours resembling a spline plane curve depicted as an asteroid, aligned with major street grid patterns. Further, Greenstein found that convex diamond-shaped RF propagation loss contours were a common occurrence in field measurements in a rectilinear urban area. The special plane curve asteroid is represented by the formula x2/3+y2/3=r2/3. However, these results alone have not been sufficiently robust and general to accurately locate an MS, due to the variable nature of urban clutter spatial arrangements.
At Telesis Technology in 1994 Howard Xia, et al, authored “Microcellular Propagation Characteristics for Personal Communications in Urban and Suburban Environments”, in IEEE Transactions of Vehicular Technology, Vol. 43, No. 3, August 1994, which performed measurements specifically in the PCS 1.8 to 1.9 GHz frequency band. Xia found corresponding but more variable outcome results in San Francisco, Oakland (urban) and the Sunset and Mission Districts (suburban).
Summary of Factors Affecting RF Propagation
The physical radio propagation channel perturbs signal strength, frequency (causing rate changes, phase delay, signal to noise ratios (eg., C/I for the analog case, or Eb/No, RF energy per bit, over average noise density ratio for the digital case) and Doppler-shift. Signal strength is usually characterized by:                Free Space Path Loss (Lp)        Slow fading loss or margin (Lslow)        Fast fading loss or margin (Lfast)        
Loss due to slow fading includes shadowing due to clutter blockage (sometimes included in Lp). Fast fading is composed of multipath reflections which cause: 1) delay spread; 2) random phase shift or Rayleigh fading; and 3) random frequency modulation due to different Doppler shifts on different paths.
Summing the path loss and the two fading margin loss components from the above yields a total path loss of:Ltotal=Lp+Lslow+Lfast Referring to FIG. 3, the figure illustrates key components of a typical cellular and PCS power budget design process. The cell designer increases the transmitted power PTX by the shadow fading margin Lslow which is usually chosen to be within the 1–2 percentile of the slow fading probability density function (PDF) to minimize the probability of unsatisfactorily low received power level PRX at the receiver. The PRX level must have enough signal to noise energy level (e.g., 10 dB) to overcome the receiver's internal noise level (e.g., −118 dBm in the case of cellular 0.9 GHz), for a minimum voice quality standard. Thus in the example PRX must never be below −108 dBm, in order to maintain the quality standard.
Additionally the short term fast signal fading due to multipath propagation is taken into account by deploying fast fading margin Lfast, which is typically also chosen to be a few percentiles of the fast fading distribution. The 1 to 2 percentiles compliments other network blockage guidelines. For example the cell base station traffic loading capacity and network transport facilities are usually designed for a 1–2 percentile blockage factor as well. However, in the worst-case scenario both fading margins are simultaneously exceeded, thus causing a fading margin overload.
In Roy, Steele's, text, Mobile Radio Communications, IEEE Press, 1992, estimates for a GSM system operating in the 1.8 GHz band with a transmitter antenna height of 6.4 m and an MS receiver antenna height of 2 m, and assumptions regarding total path loss, transmitter power would be calculated as follows:
TABLE IGSM Power Budget ExampleParameterdBm valueWill requireLslow14Lfast7L1path110Min. RX pwr required−104TXpwr = 27 dBmSteele's sample size in a specific urban London area of 80,000 LOS measurements and data reduction found a slow fading variance ofσ=7 dBassuming log normal slow fading PDF and allowing for a 1.4% slow fading margin overload, thusslow=2σ=14 dBThe fast fading margin was determined to be:Lfast=7 dB
In contrast, Xia's measurements in urban and suburban California at 1.8 GHz uncovered flat-land shadow fades on the order of 25–30 dB when the mobile station (MS) receiver was traveling from LOS to non-LOS geometries. In hilly terrain fades of +5 to −50 dB were experienced. Thus it is evident that attempts to correlate signal strength with MS ranging distance suggest that error ranges could not be expected to improve below 14 dB, with a high side of 25 to 50 dB. Based on 20 to 40 dB per decade, Corresponding error ranges for the distance variable would then be on the order of 900 feet to several thousand feet, depending upon the particular environmental topology and the transmitter and receiver geometries.